A Convergent Algorithm for Bi-orthogonal Nonnegative Matrix Tri-Factorization

TL;DR

This paper introduces a new convergent algorithm for bi-orthogonal nonnegative matrix tri-factorization, enhancing clustering capabilities with guaranteed convergence to a stationary point.

Contribution

It develops a novel algorithm based on previous techniques, ensuring convergence for bi-orthogonal NMF, which was not guaranteed in earlier multiplicative update methods.

Findings

Algorithm guarantees convergence to a stationary point.

Improves clustering performance over previous NMF methods.

Provides theoretical proof of convergence.

Abstract

A convergent algorithm for nonnegative matrix factorization with orthogonality constraints imposed on both factors is proposed in this paper. This factorization concept was first introduced by Ding et al. with intent to further improve clustering capability of NMF. However, as the original algorithm was developed based on multiplicative update rules, the convergence of the algorithm cannot be guaranteed. In this paper, we utilize the technique presented in our previous work to develop the algorithm and prove that it converges to a stationary point inside the solution space.